Argument maps are commonly used in the context of teaching and applying critical thinking.[2] The purpose of mapping is to uncover the logical structure of arguments, identify unstated assumptions, evaluate the support an argument offers for a conclusion, and aid understanding of debates. Argument maps are often designed to support deliberation of issues, ideas and arguments in wicked problems.[3]

A number of different kinds of argument map have been proposed but the most common, which Chris Reed and Glenn Rowe called the standard diagram,[5] consists of a tree structure with each of the reasons leading to the conclusion. There is no consensus as to whether the conclusion should be at the top of the tree with the reasons leading up to it or whether it should be at the bottom with the reasons leading down to it.[5] Another variation diagrams an argument from left to right.[6]

According to Doug Walton and colleagues, an argument map has two basic components: "One component is a set of circled numbers arrayed as points. Each number represents a proposition (premise or conclusion) in the argument being diagrammed. The other component is a set of lines or arrows joining the points. Each line (arrow) represents an inference. The whole network of points and lines represents a kind of overview of the reasoning in the given argument..."[7] With the introduction of software for producing argument maps, it has become common for argument maps to consist of boxes containing the actual propositions rather than numbers referencing those propositions.

There is disagreement on the terminology to be used when describing argument maps,[8] but the standard diagram contains the following structures:

Dependent premises or co-premises, where at least one of the joined premises requires another premise before it can give support to the conclusion: An argument with this structure has been called a linked argument.[9]

Statements 1 and 2 are dependent premises or co-premises

Independent premises, where the premise can support the conclusion on its own: Although independent premises may jointly make the conclusion more convincing, this is to be distinguished from situations where a premise gives no support unless it is joined to another premise. Where several premises or groups of premises lead to a final conclusion the argument might be described as convergent. This is distinguished from a divergent argument where a single premise might be used to support two separate conclusions.[10]

Statements 2, 3, 4 are independent premises

Intermediate conclusions or sub-conclusions, where a claim is supported by another claim that is used in turn to support some further claim, i.e. the final conclusion or another intermediate conclusion: In the following diagram, statement 4 is an intermediate conclusion in that it is a conclusion in relation to statement 5 but is a premise in relation to the final conclusion, i.e. statement 1. An argument with this structure is sometimes called a complex argument. If there is a single chain of claims containing at least one intermediate conclusion, the argument is sometimes described as a serial argument or a chain argument.[11]

Statement 4 is an intermediate conclusion or sub-conclusion

Each of these structures can be represented by the equivalent "box and line" approach to argument maps. In the following diagram, the contention is shown at the top, and the boxes linked to it represent supporting reasons, which comprise one or more premises. The green arrow indicates that the two reasons support the contention:

A box and line diagram

Argument maps can also represent counterarguments. In the following diagram, the two objections weaken the contention, while the reasons support the premise of the objection:

A written text can be transformed into an argument map by following a sequence of steps. Monroe Beardsley's 1950 book Practical Logic recommended the following procedure:[12]

Separate statements by brackets and number them.

Put circles around the logical indicators.

Supply, in parenthesis, any logical indicators that are left out.

Set out the statements in a diagram in which arrows show the relationships between statements.

A diagram of the example from Beardsley's Practical Logic

Beardsley gave the first example of a text being analysed in this way:

Though ① [people who talk about the "social significance" of the arts don’t like to admit it], ② [music and painting are bound to suffer when they are turned into mere vehicles for propaganda]. For③ [propaganda appeals to the crudest and most vulgar feelings]: (for)④ [look at the academic monstrosities produced by the official Nazi painters]. What is more important, ⑤ [art must be an end in itself for the artist], because⑥ [the artist can do the best work only in an atmosphere of complete freedom].

Beardsley said that the conclusion in this example is statement ②. Statement ④ needs to be rewritten as a declarative sentence, e.g. "Academic monstrosities [were] produced by the official Nazi painters." Statement ① points out that the conclusion isn't accepted by everyone, but statement ① is omitted from the diagram because it doesn't support the conclusion. Beardsley said that the logical relation between statement ③ and statement ④ is unclear, but he proposed to diagram statement ④ as supporting statement ③.

A box and line diagram of Beardsley's example, produced using Harrell's procedure

More recently, philosophy professor Maralee Harrell recommended the following procedure:[13]

Argument maps are useful not only for representing and analyzing existing writings, but also for thinking through issues as part of a problem-structuring process or writing process.[14] The use of such argument analysis for thinking through issues has been called "reflective argumentation".[15]

An argument map, unlike a decision tree, does not tell how to make a decision, but the process of choosing a coherent position (or reflective equilibrium) based on the structure of an argument map can be represented as a decision tree.[16]

In the Elements of Logic, which was published in 1826 and issued in many subsequent editions,[17] Archbishop Richard Whately gave probably the first form of an argument map, introducing it with the suggestion that "many students probably will find it a very clear and convenient mode of exhibiting the logical analysis of the course of argument, to draw it out in the form of a Tree, or Logical Division".

However, the technique did not become widely used, possibly because for complex arguments, it involved much writing and rewriting of the premises.

Wigmore evidence chart, from 1905

Legal philosopher and theorist John Henry Wigmore produced maps of legal arguments using numbered premises in the early 20th century,[18] based in part on the ideas of 19th century philosopher Henry Sidgwick who used lines to indicate relations between terms.[19]

Dealing with the failure of formal reduction of informal argumentation, English speaking argumentation theory developed diagrammatic approaches to informal reasoning over a period of fifty years.

Monroe Beardsley proposed a form of argument diagram in 1950.[12] His method of marking up an argument and representing its components with linked numbers became a standard and is still widely used. He also introduced terminology that is still current describing convergent, divergent and serial arguments.

Stephen Toulmin, in his groundbreaking and influential 1958 book The Uses of Argument,[20] identified several elements to an argument which have been generalized. The Toulmin diagram is widely used in educational critical teaching.[21][22] Whilst Toulmin eventually had a significant impact on the development of informal logic he had little initial impact and the Beardsley approach to diagramming arguments along with its later developments became the standard approach in this field. Toulmin introduced something that was missing from Beardsley's approach. In Beardsley, "arrows link reasons and conclusions (but) no support is given to the implication itself between them. There is no theory, in other words, of inference distinguished from logical deduction, the passage is always deemed not controversial and not subject to support and evaluation".[23] Toulmin introduced the concept of warrant which "can be considered as representing the reasons behind the inference, the backing that authorizes the link".[24]

Beardsley's approach was refined by Stephen N. Thomas, whose 1973 book Practical Reasoning In Natural Language[25] introduced the term linked to describe arguments where the premises necessarily worked together to support the conclusion.[26] However, the actual distinction between dependent and independent premises had been made prior to this.[26] The introduction of the linked structure made it possible for argument maps to represent missing or "hidden" premises. In addition, Thomas suggested showing reasons both for and against a conclusion with the reasons against being represented by dotted arrows. Thomas introduced the term argument diagram and defined basic reasons as those that were not supported by any others in the argument and the final conclusion as that which was not used to support any further conclusion.

Scriven's argument diagram. The explicit premise 1 is conjoined with additional unstated premises a and b to imply 2.

Michael Scriven further developed the Beardsley-Thomas approach in his 1976 book Reasoning.[27] Whereas Beardsley had said "At first, write out the statements...after a little practice, refer to the statements by number alone"[28] Scriven advocated clarifying the meaning of the statements, listing them and then using a tree diagram with numbers to display the structure. Missing premises (unstated assumptions) were to be included and indicated with an alphabetical letter instead of a number to mark them off from the explicit statements. Scriven introduced counterarguments in his diagrams, which Toulmin had defined as rebuttal.[29] This also enabled the diagramming of "balance of consideration" arguments.[30]

In 1998 a series of large-scale argument maps released by Robert E. Horn stimulated widespread interest in argument mapping.[31]

You usually think of an argument as a serial sequence of steps of reason, beginning with known facts, assumptions, etc., and progressing toward a conclusion. Well, we do have to think through these steps serially, and we usually do list the steps serially when we write them out because that is pretty much the way our papers and books have to present them—they are pretty limiting in the symbol structuring they enable us to use. ... To help us get better comprehension of the structure of an argument, we can also call forth a schematic or graphical display. Once the antecedent-consequent links have been established, the computer can automatically construct such a display for us.

In the middle to late 1980s, hypertextsoftware applications that supported argument visualization were developed, including NoteCards and gIBIS; the latter generated an on-screen graphical hypertextual map of an issue-based information system, a model of argumentation developed by Werner Kunz and Horst Rittel in the 1970s.[33] In the 1990s, Tim van Gelder and colleagues developed a series of software applications that permitted an argument map's premises to be fully stated and edited in the diagram, rather than in a legend.[34] Van Gelder's first program, Reason!Able, was superseded by two subsequent programs, bCisive and Rationale.[35]

Throughout the 1990s and 2000s, many other software applications were developed for argument visualization. By 2013, more than 60 such software systems existed.[36] One of the differences between these software systems is whether collaboration is supported.[37] Single-user argumentation systems include Convince Me, iLogos, LARGO, Athena, Araucaria, and Carneades; small group argumentation systems include Digalo, QuestMap, Compendium, Belvedere, and AcademicTalk; community argumentation systems include Debategraph and Collaboratorium.[37] For more software examples, see: § External links.

It has traditionally been hard to separate teaching critical thinking from the philosophical tradition of teaching logic and method, and most critical thinking textbooks have been written by philosophers. Informal logic textbooks are replete with philosophical examples, but it is unclear whether the approach in such textbooks transfers to non-philosophy students.[21] There appears to be little statistical effect after such classes. Argument mapping, however, has a measurable effect according to many studies.[42] For example, instruction in argument mapping has been shown to improve the critical thinking skills of business students.[43]

There is empirical evidence that the skills developed in argument-mapping-based critical thinking courses substantially transfer to critical thinking done without argument maps. Alvarez's meta-analysis found that such critical thinking courses produced gains of around 0.70 SD, about twice as much as standard critical-thinking courses.[44] The tests used in the reviewed studies were standard critical-thinking tests.

The use of argument mapping has occurred within a number of disciplines, such as philosophy, management reporting, military and intelligence analysis, and public debates.[38]

Logical structure: Argument maps display an argument's logical structure more clearly than does the standard linear way of presenting arguments.

Critical thinking concepts: In learning to argument map, students master such key critical thinking concepts as "reason", "objection", "premise", "conclusion", "inference", "rebuttal", "unstated assumption", "co-premise", "strength of evidence", "logical structure", "independent evidence", etc. Mastering such concepts is not just a matter of memorizing their definitions or even being able to apply them correctly; it is also understanding why the distinctions these words mark are important and using that understanding to guide one's reasoning.

Visualization: Humans are highly visual and argument mapping may provide students with a basic set of visual schemas with which to understand argument structures.

More careful reading and listening: Learning to argument map teaches people to read and listen more carefully, and highlights for them the key questions "What is the logical structure of this argument?" and "How does this sentence fit into the larger structure?" In-depth cognitive processing is thus more likely.

More careful writing and speaking: Argument mapping helps people to state their reasoning and evidence more precisely, because the reasoning and evidence must fit explicitly into the map's logical structure.

Literal and intended meaning: Often, many statements in an argument do not precisely assert what the author meant. Learning to argument map enhances the complex skill of distinguishing literal from intended meaning.

Externalization: Writing something down and reviewing what one has written often helps reveal gaps and clarify one's thinking. Because the logical structure of argument maps is clearer than that of linear prose, the benefits of mapping will exceed those of ordinary writing.

Anticipating replies: Important to critical thinking is anticipating objections and considering the plausibility of different rebuttals. Mapping develops this anticipation skill, and so improves analysis.

The Argument Interchange Format, AIF, is an international effort to develop a representational mechanism for exchanging argument resources between research groups, tools, and domains using a semantically rich language.[45] AIF-RDF is the extended ontology represented in the Resource Description Framework Schema (RDFS) semantic language. Though AIF is still something of a moving target, it is settling down.[46]

The Legal Knowledge Interchange Format (LKIF),[47] developed in the European ESTRELLA project,[48] is an XML schema for rules and arguments, designed with the goal of becoming a standard for representing and interchanging policy, legislation and cases, including their justificatory arguments, in the legal domain. LKIF builds on and uses the Web Ontology Language (OWL) for representing concepts and includes a reusable basic ontology of legal concepts.